Respuesta :

Answer:

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Step-by-step explanation:

To compare fractions, we need to make sure that both fractions have the same denominator. For example, for question 4, the least common multiple of 5 and 3 is 15, so we need to multiply both fractions by some numbers to get the denominators equal to 15. In this case, we will multiply the first fraction, [tex]\frac{3}{5}[/tex] by 3 to get [tex]\frac{9}{15}[/tex] and the second fraction, [tex]\frac{3}{3}[/tex] by 5 to get [tex]\frac{15}{15}[/tex].

Once we have the same denominator, we can simply compare the value of the numerators and see which one is larger. For question 4, since 9 is smaller than 15, the first fraction is smaller than the second. So the correct inequality to represent this would be "<".

To do these sums, we have to first convert them to like fractions.

For the first one:

  • LCM of denominators 5 and 3 is 15.
  • [tex] \frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15} [/tex]
  • [tex] \frac{3}{3} = \frac{3 \times 5}{3 \times 5} = \frac{15}{15} [/tex]
  • Since,
  • [tex] \frac{9}{15} < \frac{15}{15} [/tex]
  • Therefore,
  • [tex] \frac{3}{5} < \frac{3}{3} [/tex]

For the second sum:

  • LCM of denominators 6 and 8 is 24.
  • [tex] \frac{4}{6} = \frac{4 \times 4}{6 \times 4} = \frac{16}{24} [/tex]
  • [tex] \frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24} [/tex]
  • Since
  • [tex] \frac{16}{24} < \frac{21}{24} [/tex]
  • Therefore,
  • [tex] \frac{4}{6} < \frac{7}{8} [/tex]

For the third one:

  • LCM of denominators 10 and 5 is 10.
  • [tex] \frac{6}{10} = \frac{6 \times 1}{10 \times 1} = \frac{6}{10} [/tex]
  • [tex] \frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10} [/tex]
  • Since,
  • [tex] \frac{6}{10} > \frac{4}{10} [/tex]
  • Therefore,
  • [tex] \frac{6}{10} > \frac{2}{5} [/tex]

Hope you could get an idea from here.

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